3.1 Density
9 exam questions worth 22 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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A metal cube has a mass of 8.0 kg and a volume of 0.0010 m³. Calculate its density. Give the unit.
Mark scheme
ρ = m / V (1); 8.0 / 0.0010 (1); 8000 kg/m³ (1)
Model answer
ρ = m / V = 8.0 / 0.0010 = 8000 kg/m³.
Aluminium has a density of 2700 kg/m³. Calculate the mass of an aluminium block of volume 0.0020 m³.
Mark scheme
m = ρ V (1); 2700 × 0.0020 (1); 5.4 kg (1)
Model answer
m = ρ V = 2700 × 0.0020 = 5.4 kg.
A block has a mass of 500 g and a volume of 250 cm³. Calculate its density in g/cm³ and in kg/m³.
Mark scheme
500 / 250 = 2 g/cm³ (1); 2000 kg/m³ (1)
Model answer
ρ = 500 / 250 = 2 g/cm³, which is 2000 kg/m³.
Use the particle model to explain why a solid has a much higher density than a gas.
Mark scheme
the particles in a solid are close together (1); the particles in a gas are far apart (1); so in the same volume there are many more particles / more mass in a solid than a gas (1)
Model answer
The particles in a solid are close together, but the particles in a gas are far apart. So a given volume of solid contains many more particles, and therefore more mass, than the same volume of gas.
A sealed container of liquid is heated and the liquid expands. Explain what happens to its density.
Mark scheme
the mass stays the same and the volume increases (1); so the density decreases (1)
Model answer
The mass stays the same but the volume increases, so the density decreases.
Which of these is a unit of density?
Choose one answer.
Correct Not quite: the answer is kg/m³
Mark scheme
A: kg/m³
Model answer
kg/m³ (A), because density is mass divided by volume.
A block of lead has a mass of 2.26 kg. The density of lead is 11 300 kg/m³. Calculate the volume of the block in cm³.
Mark scheme
V = m ÷ ρ (1); 2.26 ÷ 11 300 = 2.0 × 10⁻⁴ m³ (1); 200 cm³ (1)
Model answer
V = m / ρ = 2.26 / 11 300 = 2.0 × 10⁻⁴ m³ = 200 cm³.
Explain why a hot-air balloon rises.
Mark scheme
the air in the balloon is heated and expands (1); the mass stays the same but the volume increases, so the density decreases (1); the hot air is less dense than the air around the balloon, so the balloon rises / floats (1)
Model answer
The air inside is heated, so it expands. The mass does not change but the volume increases, so the density falls. The balloon rises because the air inside it is less dense than the air outside.
Ice floats on water. Explain this, using ideas about density.
Mark scheme
ice is less dense than water (1); because it takes up a larger volume for the same mass (water expands as it freezes) (1)
Model answer
Ice is less dense than liquid water, since water expands when it freezes, so the same mass takes up a larger volume.
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